What's on Back POW

IAG 1H POW # 5: What's on Back?

Problem Statement

Not necessary to do.

Process

I started out on this POW thinking that you have a fifty-fifty chance all of the time. This was not true.

As I started making my bag, a few “cheap” strategies came into my head. I figured I could make corners. I could recognize how many X’s were on the sides which were lined. (I ended up using unlined cards. Finally, I realized that you could recognize imperfections of the way in which you write the letters. Next, I figured out that the front and back are interchangeable.

I started working getting trials by picking cards out of a bag. I didn’t have any specific strategy, I was just pulling cards. I recorded the pulls as follows: The front; what I thought was on the back; Correct (1) or not (0). I was correct 9/16 times.

I then started trying to use a strategy. I tried guessing the same. I was correct 8/10 times in that section. Overall, when I guessed the same, I was correct 17/23 times. To find the theoretical probity, I drew 3 cards, an X X O. I then flipped them over, on the other side respectfully was a X O O. 2 out of 3 were the same. I then shook the bag around and picked 3 more cards: X O O. On back were: X O X. 2 out of 3 were the same again. Therefore, I can conclude that guessing the same gives you a 2/3 chance of being correct. I can also conclude that picking different gives you a 1/3 chance of being correct, because it is the opposite of choosing the same.

I then tried another strategy, picking always X. In that section I was correct 6/11 times, which is also very close to half. Then, to find the theoretical probity, I picked 3 cards again: O X X, and on the back was O X O. If I picked X, I would have 1/3. I picked 3 cards again: O X O. On the back was: O X X. If I picked X, I would have 3/6 or ½ chance of being right. This means that always picking X gives you a fifty- fifty chance of being right. I suspect the same is true for always O.

Experiment

Front	Back ???	Correct
	Expermented----------------
O	O	1
O	X	1
O	O	1
O	O	0
O	X	0
O	X	1
O	X	0
O	O	1
X	O	1
O	X	0
X	X	0
X	X	1
X	O	0
O	O	0
O	O	1
O	O	1
	Guess Same---------------------------
X	X	0
X	X	1
X	X	1
X	X	1
O	O	1
O	O	0
X	X	1
O	O	1
X	X	1
O	O	1
	Guessed X------------------
O	X	1
O	X	0
X	X	0
X	X	1
X	X	0
O	X	0
X	X	1
O	X	0
X	X	1
O	X	1
X	X	1